FieldSweep：永久磁石の配列とスマートフォン磁気センサを用いた二次元トラッキング手法
理学専攻・情報科学コース 1940659 宮武

陽子（指導教員：椎尾一郎）

Figure 1: (a)A magnets arrangement used for
FieldSweep system. (b)The tracking. (c)Application
example (Magnifying glass).

1

INTRODUCTION

Figure 2: Magnet patterns proposed in our method.

Our lives are ﬁlled with information. Information provided in public places, such as station signs,maps, school bulletin boards, and billboards, is often printed on paper or boards and displayed on aﬂat surface. In recent years, the price of LCDs andprojectors has decreased, and more and more information is presented via digital signage. For example,
many information boards and vending machines withtouch panels have been installed in cities.
Many of these interactive systems are based on theuse of hand and ﬁnger movements. Therefore, there
is a growing demand for technology to detect themotion of objects on a plane. In the past, capacitive touch panels, cameras, and infrared sensors weremainly used for this detection. However, they areexpensive and require a power source, making it difﬁcult to deploy them ubiquitously.
In this paper, we propose FieldSweep, a tracking
method on a ﬂat surface using only permanent magnets and a smartphone. This method tracks the position of the smartphone as it slides above the permanent magnets (Fig.1). The basic mechanism isto measure the magnetic ﬁeld created on the planeby the permanent magnets using a three-axis magnetic sensor on the smartphone, and to estimate
the relative position to the magnets from the threedimensional vector of the measured magnetic ﬁeldlines. Since only a permanent magnets and a ﬁxing
plate, such as an acrylic plate, are used on the planeside, no electronic components or power supply arerequired.

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FIELDSWEEP

2.1

Tracking Principle

measure the directional vector of the magnetic ﬁeld
using the built-in three-axis magnetometer. The angle of the measured vector is compared with the simulated data. The location of the data with the closest
angle is considered as the position of the magnetometer. The closeness of the angle is indicated by the cosine similarity between the simulated vector and themeasured one.

2.2

Magnets Arrangement

In our method, the sensor is calibrated with theambient magnetic ﬁeld because it constitutes noisein the measurement. The ambient magnetic ﬁeld
is measured before tracking starts, and its value issubtracted from the measured value during tracking. Therefore, the intended magnetic ﬁeld by themagnets should be suﬃciently larger than the ambient magnetic ﬁeld, to perform stable measurement.
We perceived that an approximately 2 times stronger
magnetic ﬁeld is needed for stable tracking throughour study. Thus, it is desirable that the magnets arearranged so that the magnetic ﬁeld intensity is large
enough all around the tracking ﬁeld.
Furthermore, the magnetic vectors must be in different directions at each location to uniquely determine the position. To achieve stable tracking by thismethod, the magnets are placed with these two points
in mind.
In order to expand a single magnet’s magnetic ﬁeld
pattern to a large area, we considered two types ofextension method. One method is the repetitive expansion shown in Fig.2(b) and (b’). By arranging themagnets in a checkerboard pattern with the N and Spoles facing forward, the magnetic ﬁeld area that canbe measured with a smartphone can be extended toa larger area (Fig.2(b)). Here, the yellow square in
the ﬁgure is one unit, and the magnet arrangement
is repeated left to right, and up and down. Hereinafter, this unit is referred to as a repetitive unit.
The repetitive units have exactly the same magnetic

In FieldSweep, we ﬁrst store the magnetic vector
ﬁeld data of the plane above the magnets. The magnets are conﬁgured in a speciﬁc pattern. The data isa two-dimensional array of three-dimensional vector
values. Next, we construct the actual magnet conﬁguration and place a smartphone on the plane at adistance corresponding to the simulation. Then we1

for each grid point is shown in Figure 3. In pattern (a’), the average error over the entire area was
27.6mm, and in pattern (b’) it was 11.1mm. The errors for one side of the measurement area were 12%
for pattern (a’) and 9% for pattern (b’), which meansthat the position could be detected with an error ofabout 10% each.

3

Various technologies have been developed for tracking and input using magnets. In particular, permanent magnets, which do not require a powersource and are inexpensive, are often used in humancomputer interaction (HCI) research because they
are easy to use and readily available[3][1].
Also, various techniques for two-dimensional tracking have been studied. For example, optical sensors,cameras, or capacitive sensors are used. These methods require a power supply and installation cost.
Some methods use hand-held machines or sensors
for tracking, like our method. For example, mechanical and optical mouse methods have been proposed
for interaction to detect object movement. However,since these methods can only estimate relative movement, the initial position must be speciﬁed. Some
research used a capacitive touch panel or an LCD
to track mobile devices on a planer surface[2]. Our
method does not require special patterns for the surface and only requires a smartphone as the handheldmachine.

Figure 3: Results of accuracy evaluation. The average error [mm] for each grid point is shown. Pattern(a’) on the left and pattern (b’) on the right. The
black ﬁgures show the magnet position.
ﬁeld pattern, so the magnetic vector can be uniqueonly in one repetitive unit. Therefore, the absolute
position can only be estimated within this one unit.
Furthermore, we assumed that we can use a magnet
array called a Halbach array[4] to expand the rangeof the magnetic ﬁeld further. In the Halbach array, ahorizontal magnet is inserted between each magnet.
The magnetic ﬁeld on the top surface is enhanced by
the interference of the vertical and horizontal magnets. We used this idea to expand a magnetic ﬁeld
further, for Fig.2(a) and (b) each. They are shownin Fig.2(a’) and (b’), respectively. In the following,
we refer to them as pattern (a’) and pattern (b’),
respectively.
In pattern (a’), a single magnet’s magnetic ﬁeld
was enlarged to a circular pattern. The magnets areplaced horizontally to strengthen the magnetic ﬁeld
on the upper surface, using the idea of the Halbach
array.
In pattern (b’), we used the Halbach array again toexpand the size of one repetitive unit of the checkerboard pattern. A horizontal magnet was placed between each of the upward-facing magnets. This arrangement generates a suﬃcient magnetic ﬁeld on
the tracking surface even when the magnet spacing iswidened. As a result, the repetitive unit range can belarge, compared with a simple checkerboard pattern.

2.3

RELATED WORK

4CONCLUSION

This paper presents FieldSweep, a two-dimensional
tracking method using only a smartphone and inexpensive permanent magnets. This method requires
no external power supply, no electronic components,and no attachments to the smartphone.

References[1] Ke-Yu Chen, Kent Lyons, Sean White, andShwetak Patel. UTrack: 3D Input Using Two
Magnetic Sensors. In Proc. of UIST. 237–244.

Tracking Accuracy Evaluation

We conducted an experiment to evaluate the accuracy of the tracking for patterns (a’) and (b’).
We prepared a grid of points with 40mm spacing
for pattern (a’) and 20mm spacing for pattern (b’)
from edge to edge of the board, and measured thedistance between the estimated position and the actual position at each point.
The initial position was arbitrarily selected fromthe measurement target area. After the initial position estimation, the smartphone was moved so thatthe sensor of the smartphone was positioned directly
above the grid point to be measured, and the position
was estimated. The above procedure was carried out
ﬁve times in total.
The error (the distance from the original coordinates to the measured point) averaged over all trials[2] Sang-won Leigh, Philipp Schoessler, Felix
Heibeck, Pattie Maes, and Hiroshi Ishii. 2015.
THAW: Tangible Interaction with See-ThroughAugmentation for Smartphones on Computer
Screens. In Proc. of TEI. 89–96.
[3] Rong-Hao Liang, Kai-Yin Cheng, Chao-Huai
Su, Chien-Ting Weng, Bing-Yu Chen, and DeNian Yang. 2012. GaussSense: Attachable Stylus Sensing Using Magnetic Sensor Grid. In
Proc. of UIST. 319–326.
[4] J. Mallinson. 1973. One-sided ﬂuxes – A magnetic curiosity? IEEE Transactions on Magnetics 9 (1973), 678–682.

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